Method for performing automated in-scene based atmospheric compensation for multi-and hyperspectral imaging sensors in the solar reflective spectral region

ABSTRACT

A method of automatically compensating a multi- or hyper-spectral, multi-pixel image for atmospheric effects, comprising resolving a plurality of spectrally-diverse pixels from the image, determining a spectral baseline from the spectrally-diverse pixels, determining a statistical spectral deviation of the spectrally-diverse pixels, normalizing the statistical spectral deviation by applying a scale factor, and compensating image pixels with both the spectral baseline and the normalized spectral deviation. Another embodiment features a method of automatically determining a measure of atmospheric aerosol optical properties using a multi- or hyper-spectral, multi-pixel image, comprising resolving a plurality of spectrally-diverse pixels from the image, determining a statistical spectral deviation of the spectrally-diverse pixels, correcting the statistical spectral deviation for non-aerosol transmittance losses, and deriving from the statistical spectral deviation one or more wavelength-dependent aerosol optical depths. A final embodiment features a method of automatically determining a measure of atmospheric gaseous optical properties using a multi- or hyper-spectral, multi-pixel image, comprising resolving a plurality of spectrally-diverse pixels from the image, determining a statistical spectral deviation of the spectrally-diverse pixels, and deriving from the statistical spectral deviation wavelength-dependent gaseous optical depths.

GOVERNMENT RIGHTS

This invention was made with Government support under ContractF19628-02-C-0054 awarded by the Department of the Air Force. TheGovernment has certain rights in this invention.

FIELD OF INVENTION

This invention relates to automated methods for correcting multi- andhyperspectral images of the earth's surfaces for atmospheric effects andsensor calibration problems.

BACKGROUND OF THE INVENTION

The problem addressed here is the compensation of remotely sensed multi-and hyperspectral images in the solar reflective spectral regime (λ<3000nm) for the transmission losses and scattering effects of theintervening atmosphere. The problem is illustrated in FIG. 1 for a pixelcontaining vegetation as viewed from a space-based sensor. A number oflarge spectral depressions are seen which are primarily due toabsorption by gaseous water and to a lesser extent by carbon dioxide andoxygen. Below 700 nm, the observed reflectance exceeds the actualreflectance; this is due to atmospheric scattering by aerosols andmolecules. The apparent reflectance at the sensor is well represented byρ_(j)(λ)=A(λ)+B(λ)ρ_(j) ^(o)(λ)+C(λ)<ρ(λ)>,  (1)where ρ_(j) is the observed reflectance (the radiance normalized by thesurface normal component of the solar flux) for the j'th pixel at aspectral band centered at wavelength λ, ρ_(j) ^(o) is the actual surfacereflectance, <ρ> is a spatially averaged surface reflectance, and A, B,and C are coefficients representing the transmission and scatteringeffects of the atmosphere. The first coefficient, A, accounts for lightwhich never encounters the surface and is scattered and absorbed withinthe atmosphere. The second, B, accounts for the sun-surface-sensor pathtransmittance loss. The third, C, accounts for the adjacency effectwhich is the cross talk between pixels induced by atmosphericscattering. The length scale of the adjacency effect is typically oforder ˜0.5 km, thus <ρ> is a slowly varying function of position withina large image. It is noted that B and C also have a weak dependence on<ρ> through light that reflects off the surface and is scattered back tothe surface by the atmosphere.

The aim of atmospheric compensation is to determine A, B, C and <ρ> bysome means in order to invert Eq(1) to retrieve the actual surfacereflectance, ρ_(j) ^(o). The prior art is embodied in various methodsdescribed in the literature and summarized below.

The simplest and computationally fastest prior art methods foratmospheric correction are the “Empirical Line Method” (ELM) andvariants thereof, which may be found in the ENVI (Environment forVisualizing Images) software package of Research Systems, Inc. The ELMassumes that the radiance image contains some pixels of knownreflectance, and also that the radiance and reflectance values for eachwavelength channel of the sensor are linearly related, in theapproximation that A, B, C and <ρ> are constants of the image.Therefore, the image can be converted to reflectance by applying asimple gain and offset derived from the known pixels. This method ishowever not generally applicable, as in-scene known reflectances areoften not available. In variants of the ELM, approximate gain and offsetvalues are generated using pixels in the image that are treated as iftheir spectra were known. For example, in the Flat Field Method a singlebright pixel is taken as having a spectrally flat reflectance and theoffset is taken as zero; accordingly, dividing the image pixel spectraby the bright pixel spectrum yields approximate relative reflectances.In the Internal Average Relative Reflectance method this procedure isfollowed using a scene-average spectrum rather than a single brightpixel spectrum. In general, neither the Flat Field Method nor theAverage Relative Reflectance methods are very accurate.

More sophisticated prior art methods are based on first-principlescomputer modeling. These methods require extensive, and oftentime-consuming, calculations with a radiative transfer code, such asMODTRAN [Berk et al., 1998], in which A, B and C are computed for a widerange of atmospheric conditions (aerosol and water column amounts anddifferent surface reflectance values). The calculations may be performedfor each image to be analyzed, or may be performed ahead of time andstored in large look-up tables. The appropriate parameter values for theimage are determined by fitting certain observed spectral features, suchas water vapor absorption bands, to the calculations. For retrievingaerosol or haze properties such as the optical depth, methods areavailable that rely on “dark” pixels, consisting of vegetation or darksoil [Kaufman et al., 1997] or water bodies. Commonly usedfirst-principles computer codes for atmospheric correction include:ATREM [Gao et al., 1996]; ACORN [R. Green, unpublished], available fromAnalytical Imaging and Geophysics LLC; FLAASH [Adler-Golden et al.,1999], developed by Spectral Sciences Inc. (SSI) and the Air ForceResearch Laboratory (AFRL); and ATCOR2 [Richter, 1996], used mainly formultispectral atmospheric correction.

SUMMARY OF THE INVENTION

The invention includes both a complete atmospheric correction method,and methods for retrieving the wavelength-dependent optical depth of theaerosol or haze and molecular absorbers. The atmospheric correctionmethod of the current invention, unlike first-principles methods, allowsthe retrieval of reasonably accurate reflectance spectra even when thesensor does not have a proper radiometric or wavelength calibration, orwhen the solar illumination intensity is unknown, such as when a clouddeck is present. The computational speed of the atmospheric correctionmethod is superior to that of first-principles methods, making itpotentially suitable for real-time applications. The inventiondetermines the atmospheric compensation parameters directly from theinformation contained within the scene (observed pixel spectra).

The aerosol optical depth retrieval method of the current invention,unlike prior art methods, does not require the presence of dark pixels.The retrieved optical depth information can be utilized to improve theaccuracy of methods that use first-principles modeling. In particular,it can be used to set the optical depth of a model aerosol when darkpixels are unavailable, or to select from among alternative modelaerosols to provide consistency between optical depths retrieved from adark pixel method and from the current invention.

The underlying assumptions of the invention are:

-   -   1. There are a number (≈10 or more) of diverse pixel spectra        (diverse materials) in the scene, and    -   2. The spectral standard deviation of ρ_(j) ^(o) for a        collection of diverse materials is a nearly        wavelength-independent constant.

An additional, helpful assumption is:

-   -   3. There are sufficiently dark pixels (ρ_(j) _(o)(λ)≈0) in a        scene to allow for a good estimation of the nearly spatially        invariant baseline contribution, ρ_(b)=A+C<ρ>.

The first assumption is virtually always applicable, as it only requiresthat a handful of pixels out of typically ˜10⁵ to 10⁶ pixels displaydiverse spectra. The most notable exception would be a scene overcompletely open and deep water, in which case the material reflectanceis well known a priori. The diverse spectra can be selected using any ofa number of spectral diversity metrics and algorithms. The secondassumption appears to be generally true based on empirical observationand is likely related to the lack of spectral correlation betweendiverse materials. The third assumption is frequently applicable, asmost scenes will contain a number of very dark pixels from such surfacesas water bodies, vegetation, and cast shadows. For the atypical casesthat violate this assumption, there are methods, described below, forestimating a reasonable baseline.

Under these assumptions, the spectral standard deviation of Eq(1) for aset of diverse pixel spectral can be expressed as,σρ(λ)=B(λ)σρ^(o)(λ).  (2)

There is no contribution to the standard deviation from A or C<ρ>because they are the same for each pixel spectrum. Since σρ^(o) isassumed to be constant, then to within a normalization factor,designated g_(o), σρ represents one of the correction factors, B. Theactual surface spectral reflectance can be retrieved using the extractedin-scene determined compensation parameters via $\begin{matrix}{{\rho_{j}^{o}(\lambda)} = {\frac{{\rho_{j}(\lambda)} - {\rho_{b}(\lambda)}}{g_{o}\sigma\quad{\rho(\lambda)}}.}} & (3)\end{matrix}$

A key attribute of this invention is its applicability to any sensorviewing or solar elevation angle.

There are a number of methods to establish the normalization factorg_(o), which depends on sensor attributes. For many sensors there is atleast one atmospheric window band, typically in the 1500-2500 nm region(see FIG. 1), for which B(λ)≈1 (inspection of FIG. 1 shows that B=0.9 isa good estimate); thus for this bandg _(o)=0.9/σρ.  (4)

If a suitable window band is not available, the normalization can stillbe extracted directly from the standard deviation curve. Two bands(λ₂>λ₁) are selected which are outside of any water absorption region,insuring that the atmospheric extinction is due primarily to theaerosols. The ratio of the standard deviations of these bands is adirect measure of the difference in aerosol optical depth τ via,$\begin{matrix}{{{- \ln}\quad\frac{\sigma\quad{\rho\left( \lambda_{1} \right)}}{\sigma\quad{\rho\left( \lambda_{2} \right)}}} = {{\tau\left( \lambda_{1} \right)} - {{\tau\left( \lambda_{2} \right)}.}}} & (5)\end{matrix}$Depending on the wavelengths of the selected bands, a generally smallcorrection for molecular Rayleigh scattering may be required. Standardand efficient methods are available for applying this correction.

For aerosols, the ratio of optical depths at two wavelengths is wellapproximated by the Angstrom formula, $\begin{matrix}{{\frac{\tau\quad\left( \lambda_{1} \right)}{\tau\quad\left( \lambda_{2} \right)} = \left( \frac{\lambda_{2}}{\lambda_{1}} \right)^{\alpha}},{\left( {\alpha > 0} \right).}} & (6)\end{matrix}$

For terrestrial aerosols α falls in the range 1>α>2, and we adopt α=1.5for general estimation purposes. Combining Eqs. (5) and (6) allows oneto convert the optical depth difference to an absolute optical depth ateither wavelength, $\begin{matrix}{{\tau\left( \lambda_{2} \right)} = {\frac{{- \ln}\quad\frac{\sigma\quad{\rho\left( \lambda_{1} \right)}}{\sigma\quad{\rho\left( \lambda_{2} \right)}}}{\left( \frac{\lambda_{2}}{\lambda_{1}} \right)^{\alpha} - 1}.}} & (7)\end{matrix}$

The normalization factor is now determined fromg _(o)=exp(−τ(λ₂))/σρ(λ₂).  (8)

It is noted that Eq(8) is just the generalization of Eq(4).

If the sensor radiometric calibration or the solar illuminationintensity are not known, then σρ is known only to within a scale factor,and the normalization factor go must be estimated by a different method.One method is to set g_(o) such that that the maximum retrievedreflectance value for any wavelength and pixel is unity. This method isfound to work reasonably in images containing a diversity of man-madematerials, such as urban scenes. Another method is to derive g_(o) bycomparing the retrieved reflectance values with those in a library ofmaterial spectra.

For most scenes, the baseline curve is defined as the darkest observedsignal for each band from among the diverse spectra. The presence ofsufficiently dark pixels is indicated by at least one pixel spectrumwith an apparent reflectance below ˜0.05 for λ>1500 nm. For the raresituation that a dark spectrum is unavailable, it is still possible toestimate a reasonable background. It is worth noting that this casearises because the pixel reflectances are generally much larger than thebaseline contribution, thus considerable uncertainty in the baselinevalues are tolerable. In this case, the baseline may be approximated asthe excess reflectance at the shorter wavelengths (where baselineeffects are most important) relative to a flat spectral reflectancematerial,ρ_(b)(λ)=ρ_(b) ^(o)(λ)−βσρ(λ), (λ<1000 nm),  (9)where ρ_(b) ^(o) is an initial baseline guess defined by the darkestavailable channels, and β is adjusted such that ρ_(b)=0 at 1000 nm (orsome suitably nearby channel depending on the available sensor bands).The baseline is taken as zero for λ>1000 nm. An alternative method is touse a radiative-transfer code to compute the baseline based on theretrieved aerosol and molecular optical properties. Other methods forestimating the baseline spectrum will be known to those skilled in theart. These include a pairwise linear regression method [Crippen, 1987]and a dark pixel method that incorporates a theoretical representationof the baseline's wavelength dependence [Chavez, 1988].

While the focus of the previous discussion was on atmosphericcompensation, it was noted that this invention provides, to within anormalization factor, the sun-surface-sensor path transmittance B(λ).Analysis of B can provide quantitative measures (column amounts) of allthe atmospheric attenuation sources, including aerosol scattering andabsorption and molecular absorption and Rayleigh scattering. This may beaccomplished through spectral fitting with an accurate atmosphericradiative-transfer code (e.g., MODTRAN), or alternatively through theuse of analytical approximations. Of most significance is that one canextract the detailed wavelength dependence of the aerosol extinctionwhich has not been accessible with previous multi- and hyperspectralimage analysis approaches.

It should be noted that the definition of a scene or image is flexible,in that it may include a sub-section of pixels from a larger originaldata set. Thus, the current invention may be applied to individualsub-sections of a scene or image, provided that a sufficient diversityof pixel spectra exists within the sub-sections for computing anaccurate standard deviation and baseline. In this way, spatialvariations in the adjacency averaged reflectance <ρ> and in theatmospheric parameters can be identified and taken into account in theatmospheric correction.

This invention features in one embodiment a method of automaticallycompensating a multi- or hyper-spectral, multi-pixel image foratmospheric effects, comprising resolving a plurality ofspectrally-diverse pixels from the image, determining a spectralbaseline from the spectrally-diverse pixels, determining a statisticalspectral deviation of the spectrally-diverse pixels, normalizing thestatistical spectral deviation by applying a scale factor, andcompensating image pixels with both the spectral baseline and thenormalized spectral deviation.

The compensating step may comprise subtracting the spectral baselinefrom the image pixels to accomplish partially-compensated pixels, andfurther, dividing the partially-compensated pixels by the normalizedspectral deviation. The resolving step may take place with a spectralend member selection algorithm or a clustering algorithm, and may beaccomplished manually. At least ten end members may be resolved. Theresolving step may take place using a subset of spectral bands that spanthe spectrum of the image.

The method may further comprise screening anomalous pixels out of theimage pixels before the resolving step. The screening step may compriseremoving pixels containing opaque clouds and cirrus clouds.

The spectral baseline determining step may take place using a linearregression method. The spectral baseline determining step may comprisedetermining the excess reflectance at relatively short wavelengthsrelative to a flat spectral reflectance material, or may comprisedetermining the darkest signal from all of the image pixels for eachspectral band, or determining the darkest signal in any spectral bandfrom all of the spectrally-diverse pixels, or subtracting a constantreflectance contribution. The spectral baseline determining step in thiscase may further comprise setting the constant reflectance contributionto match the image signal at a reference wavelength. The spectralbaseline determining step may use a radiative-transfer code to computethe baseline based on the determined aerosol and molecular opticalproperties

The statistical spectral deviation determining step may comprisedetermining the standard deviation of the spectrally-diverse pixels. Thenormalizing step may comprise normalizing in a spectral band in whichthe sun-surface-sensor path spectral transmittance factor is close tounity, or resolving at least two spectral window bands that do not havea significant contribution from water absorption, using the spectraldeviations of these window bands to retrieve an aerosol optical depth,and using the optical depth to normalize. The normalizing step mayinvolve establishing the scale factor such that the maximum retrievedreflectance value for any wavelength and pixel of the spectrally-diversepixels is unity. Alternatively, the normalizing step may comprisecomparing the spectrally-diverse pixels to a predetermined set ofspectra of different, known materials.

The image compensation method may further comprise refining thespectrally-diverse pixels to remove spectrally-diverse pixels thatcontain undesirable spectral features, the refining step taking placeafter the normalizing step and before the compensating step. Thisrefining step may comprise removing pixels with an abrupt reflectancechange around about 700 nm, or removing pixels that have the greatesteffect on the smoothness of the statistical spectral deviation, orintroducing a wavelength dependence into a normalization factor suchthat selected spectrally-diverse pixels are made to agree withcorresponding known library spectra as closely as possible.

This invention features in another embodiment a method of automaticallydetermining a measure of atmospheric aerosol optical properties using amulti- or hyper-spectral, multi-pixel image, comprising resolving aplurality of spectrally-diverse pixels from the image, determining astatistical spectral deviation of the spectrally-diverse pixels,correcting the statistical spectral deviation for non-aerosoltransmittance losses, and deriving from the statistical spectraldeviation one or more wavelength-dependent aerosol optical depths.

The statistical spectral deviation determining step may comprisedetermining the standard deviation of the spectrally-diverse pixels. Thecorrecting step may involve using a radiative transfer code. Thederiving step may also involve using a radiative transfer code. Thederiving step may alternatively comprises performing a least squares fitof the statistical spectral deviation to an analytical representation ofthe aerosol transmittance, or performing a least squares fit of thestatistical spectral deviation to a radiative transfer code.

In a final embodiment, this invention features a method of automaticallydetermining a measure of atmospheric gaseous optical properties using amulti- or hyper-spectral, multi-pixel image, comprising resolving aplurality of spectrally-diverse pixels from the image, determining astatistical spectral deviation of the spectrally-diverse pixels, andderiving from the statistical spectral deviation wavelength-dependentgaseous optical depths.

The statistical spectral deviation determining step may comprisedetermining the standard deviation of the spectrally-diverse pixels. Thederiving step may comprise selecting spectral bands that are outside ofany water absorption region, and deriving a gaseous optical depth fromthe statistical spectral deviations at the selected bands.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an example of observed and actual spectral reflectance curvesof a vegetation-containing pixel for a nadir-viewing space-based sensor,useful in understanding the invention.

FIG. 2 is a data processing flow diagram for the preferred embodiment ofthe invention;

FIG. 3 shows selected spectral end members for a particular observation;

FIG. 4 shows normalized and atmospherically compensated end members ofFIG. 3;

FIG. 5 shows the effect of the end member refinement process of thepreferred embodiment;

FIG. 6 is a comparison of atmospherically compensated hyper-spectraldata of the invention to ground truth measurements and to compensateddata based on the FLAASH code;

FIG. 7 is a comparison of atmospherically compensated multi-spectraldata of the invention to compensated data based on the FLAASH code;

FIG. 8 is a data processing flow diagram for the preferred embodiment ofthe aerosol optical properties retrieval method of the invention; and

FIG. 9 depicts examples of aerosol optical properties retrieval of theinvention for both clear and hazy data.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 2 depicts the data processing flow for the preferred embodiment.The sensor data 100 is comprised of multi- or hyperspectral imagery inwhich at least two spectral bands below 3000 nm are available. There isno upper limit to the number of spectral bands that can be handled. Theinput data can be in units of calibrated radiance or apparent spectralreflectance or even in uncalibrated raw counts. The choice of units onlyimpacts the selection of normalization method 112.

A spectral end member selection algorithm 102 is used to select aplurality of spectrally-diverse pixels. While there are a number ofsuitable end member algorithms, the Spectral Sciences, Inc. SMACC(Sequential Maximum Angle Convex Cones) algorithm was utilized for itsexcellent computational efficiency. Other methods for selecting adiverse set of pixel spectra will be known to those skilled in the art,and may include clustering algorithms as well as end member algorithms;however, clustering algorithms are usually more computationallyintensive. The precise number of end members used for the compensationis not critical. 10 to 20 end members is typically sufficient. Animportant aspect of SMACC is that it finds end members in order ofdecreasing spectral diversity. This can afford a significantcomputational efficiency, since the end member selection process can beterminated after the pre-selected number of end members is attained. Forsensors containing more than ˜10 spectral bands it is computationallyefficient to limit the end member selection process to ˜10 bands. Use ofa subset of the total available number of bands does not impact thecompensation quality as long as the selected subset spans the sensorspectral coverage.

FIG. 3 displays end members selected from data taken by the airborneAVIRIS sensor (400-2500 nm, 224 bands, 512×512 scene pixels, 2 m GSD(Ground Sampling Distance)). Note the diversity of the selected spectra,a key aspect of this invention.

It is important to screen for and eliminate anomalous pixel spectra fromthe end member selection process. This includes pixels containing opaqueclouds, thin cirrus clouds, and “bad” pixels containing sensorartifacts. Opaque clouds may be recognized using one of two methods,depending on the available sensor bands. If bands are available ineither of the 940 nm or 1140 nm water vapor absorption bands, thenopaque clouds can be recognized through anomalously small absorptiondepressions, as the clouds reside above most of the water vapor column.If the water bands are not available, then clouds can be recognizedthrough a whiteness-brightness test; they are spectrally flat (white)and exhibit a high reflectance (bright). Thin cirrus is most easilyflagged through an excess signal (cloud back scattering) in the verydark 1380 nm water absorption band. Cirrus clouds occur at much higheraltitudes than other clouds, and thus are detectable even in verystrongly absorbing water bands. Bad pixels are recognized through thepresence of anomalously high (saturated) or low (negative) spectralchannels. The screening thresholds for these types of anomalous pixelscan be set conservatively. Since a reasonably large number of endmembers are selected, it does not matter if a few legitimate spectra areeliminated in the screening process.

Spectral standard deviation and baseline determination 106 are thenperformed on the selected end members. The methods for determining thebaseline 110 and the conditions under which they are employed weredescribed above. Similarly, for calibrated data, the methods fordetermining the normalization factor g_(o) 112 were previouslydescribed. However, for uncalibrated data the normalization isdetermined and applied after the atmospheric compensation step 116. Inthis case, the brightest spectral channel from among all the compensatedend members is scaled to unit reflectance; the required scaling factoris g_(o).

Atmospheric compensation on the end members 116 is performed usingEq.(3). The resulting compensated end members 118 for the AVIRIS dataare presented in FIG. 4. At this point, an improvement in the constancyof the standard deviation may be made by refining the end memberselection 120 to remove end members that contain undesirable spectralfeatures, generally characterized by an abrupt change in reflectance.This most often occurs for vegetation, which has a sharp red edge around700 nm. As indicated in FIG. 4, there are vegetation end members for theAVIRIS data. It is straightforward to automatically identify and cullout vegetation spectra by searching for abrupt reflectance changesbetween bands on either side of the red edge. The improvement in thestandard deviation due to removal of vegetation spectra is apparent inFIG. 5.

Further refinements of the end member selection may also be made byvarious methods. One method is to require that the end members beselected to agree with spectra contained in a library, or with linearcombinations of such library spectra, to within a certain threshold. Thelibrary spectra may also be used to select or refine the value of thenormalization factor g_(o) to obtain the best fit between the normalizedend members and the library spectra. In a generalization of the fittingstep, a wavelength dependence may be introduced into the normalizationfactor g_(o) such that the selected end members are made to agree withthe corresponding library spectra as closely as possible. Another methodfor end member selection refinement is to require that the end membersobey a requirement of spectral smoothness, such as by setting an upperlimit on adjacent-channel differences; this represents a generalizationof the vegetation exclusion method.

The refined end members undergo the same standard deviation processing124 as comprised by steps 106, 108, and 112, resulting in the refinednormalized standard deviation 126. Finally, atmospheric compensation 128is performed on the entire sensor data set to yield the desired endproduct, the surface spectral reflectance data cube 130 (compensatedspectra for all the pixels). This entails subtracting the baseline anddividing by the refined normalized standard deviation. The entireprocess flow is automated. Aside from the sensor data, the onlyexternally required inputs are the solar elevation angle for each dataset and specification of the available bands (band centers and widths)for the sensor.

The quality of the atmospheric compensation for the presentationinvention can be assessed by comparison to results from one of thestate-of-the-art atmospheric compensation codes, FLAASH. This comparisonis provided in FIG. 6. FLAASH required ˜10 min of computational time toperform its analysis whereas the present invention required under 1 minon the same computer (1.8 GHz Pentium IV PC). This invention also workswell for multi-spectral satellite data such as from the Landsat7 ETM+sensor (6 bands in the 450-2500 nm region with a 30 m GSD), as shown inFIG. 7.

The preferred embodiment for the aerosol optical properties retrieval ispresented in FIG. 8. The starting point for the aerosol propertiesretrieval is the refined un-normalized standard deviation 200 whichderives from the standard deviation processing 124 (see FIG. 2) of theend members. The un-normalized standard deviation is first corrected forsun-surface-sensor transmittance losses due to Rayleigh scattering. Thismay be accomplished either through the use of an accurateradiative-transfer code (e.g., MODTRAN) or through well-established andaccurate analytical approximations. While it is generally preferred toselect bands outside of the molecular absorption bands, this is not alsopossible for some sensors. In these cases, the molecular absorptioneffects 204 can be corrected through the use of an accurateradiative-transfer code in concert with specification of the molecularabsorber column amounts. The molecular column amounts may be obtainedeither by retrieval from the un-normalized spectral standard deviation200 itself if suitable bands are available using an atmosphericcompensation code such as FLAASH or by estimation based on a climatologydata base or measured weather conditions. The aerosol optical propertiesretrieval 206 is performed on the Rayleigh scattering and molecularabsorption compensated data. It proceeds in two steps. First, the bandsselected for the aerosol retrieval are ratioed to a reference band andthe resulting ratios are fit using the Angstrom formula in Eq.(6). Thisresults in the reference optical depth τ_(o) and wavelength scalingexponent α. Second, this also enables a more exact determination of thenormalization constant using Eq.(8), which can be employed in theatmospheric compensation processing. The use of the aerosol retrievalalgorithm is illustrated in FIG. 9 for examples of clear and hazy dataobtained by the AVIRIS sensor.

The molecular optical properties for each molecular absorption featurecan also be retrieved from the un-normalized spectral standard deviation200. This requires at least three bands, a molecular absorption band andtwo nearby, preferably flanking, reference bands (no molecularabsorption). By linear interpolation or extrapolation, the referencebands are used to estimate the zero-absorption signals for eachabsorption band. The ratio of the absorption band signals to theircorresponding zero-absorption signals define the molecular transmittancefunction T(λ). The molecular optical depths can be retrieved fromτ(λ)=−lnT(λ). If the spectral absorption coefficients α(λ) are known forthe band, then the molecular column amount U can be retrieved from asingle wavelength by U=τ(λ)/α(λ).

Although specific features of the invention are shown in some drawingsand not others, this is for convenience only as some feature may becombined with any or all of the other features in accordance with theinvention.

Other embodiments will occur to those skilled in the art and are withinthe following claims:

1. A method of automatically compensating a multi- or hyper-spectral,multi-pixel image for atmospheric effects, comprising: resolving aplurality of spectrally-diverse pixels from the image; determining aspectral baseline from the spectrally-diverse pixels; determining astatistical spectral deviation of the spectrally-diverse pixels;normalizing the statistical spectral deviation by applying a scalefactor; and compensating image pixels with both the spectral baselineand the normalized spectral deviation.
 2. The image compensation methodof claim 1 wherein the compensating step comprises subtracting thespectral baseline from the image pixels to accomplishpartially-compensated pixels.
 3. The image compensation method of claim2 wherein the compensating step further comprises dividing thepartially-compensated pixels by the normalized spectral deviation. 4.The image compensation method of claim 1 wherein the resolving steptakes place with a spectral end member selection algorithm.
 5. The imagecompensation method of claim 1 wherein the resolving step takes placewith a clustering algorithm.
 6. The image compensation method of claim 1wherein the resolving step is accomplished manually.
 7. The imagecompensation method of claim 1 wherein at least ten end members areresolved.
 8. The image compensation method of claim 1 wherein theresolving step takes place using a subset of spectral bands that spanthe spectrum of the image.
 9. The image compensation method of claim 1further comprising screening anomalous pixels out of the image pixelsbefore the resolving step.
 10. The image compensation method of claim 9wherein the screening step comprises removing pixels containing clouds.11. The image compensation method of claim 1 wherein the spectralbaseline determining step takes place using a linear regression method.12. The image compensation method of claim 1 wherein the spectralbaseline determining step comprises determining the excess reflectanceat relatively short wavelengths relative to a flat spectral reflectancematerial.
 13. The image compensation method of claim 1 wherein thespectral baseline determining step comprises determining the darkestsignal from all of the image pixels for each spectral band.
 14. Theimage compensation method of claim 1 wherein the spectral baselinedetermining step comprises determining the darkest signal in anyspectral band from all of the spectrally-diverse pixels.
 15. The imagecompensation method of claim 14 wherein the spectral baselinedetermining step comprises subtracting a constant reflectancecontribution.
 16. The image compensation method of claim 15 wherein thespectral baseline determining step further comprises setting theconstant reflectance contribution to match the darkest signal at areference wavelength.
 17. The image compensation method of claim 1wherein the spectral baseline determining step is based on using aradiative-transfer code to compute the baseline based on the determinedaerosol and molecular optical properties.
 18. The image compensationmethod of claim 1 wherein the statistical spectral deviation determiningstep comprises determining the standard deviation of thespectrally-diverse pixels.
 19. The image compensation method of claim 1wherein the normalizing step comprises normalizing in a spectral band inwhich the sun-surface-sensor path spectral transmittance factor is closeto unity.
 20. The image compensation method of claim 1 wherein thenormalizing step comprises resolving at least two spectral window bandsthat do not have a significant contribution from water absorption,correcting for Rayleigh scattering, using the spectral deviations ofthese window bands to retrieve an aerosol optical depth, and using theoptical depth to normalize.
 21. The image compensation method of claim 1wherein the normalizing step involves establishing the scale factor suchthat the maximum retrieved reflectance value for any wavelength andpixel of the spectrally-diverse pixels is unity.
 22. The imagecompensation method of claim 1 wherein the normalizing step comprisescomparing the spectrally-diverse pixels to a predetermined set ofspectra of different, known materials.
 23. The image compensation methodof claim 1 further comprising refining the spectrally-diverse pixels toremove spectrally-diverse pixels that contain undesirable spectralfeatures, the refining step taking place after the normalizing step andbefore the compensating step.
 24. The image compensation method of claim23 wherein the refining step comprises removing pixels with an abruptreflectance change around about 700 nm.
 25. The image compensationmethod of claim 23 wherein the refining step comprises removing pixelsthat have the greatest effect on the smoothness of the statisticalspectral deviation.
 26. The image compensation method of claim 23wherein the refining step comprises introducing a wavelength dependenceinto a normalization factor such that selected spectrally-diverse pixelsare made to agree with corresponding known library spectra as closely aspossible.